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Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions

Nicolas Champagnat 1, * Sylvie Roelly 2 
* Corresponding author
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process|the conditioned multitype Feller branching diffusion are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too.
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Submitted on : Tuesday, December 9, 2008 - 4:56:23 PM
Last modification on : Tuesday, October 25, 2022 - 4:19:43 PM
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  • HAL Id : inria-00164758, version 2
  • ARXIV : 0707.3504


Nicolas Champagnat, Sylvie Roelly. Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions. Electronic Journal of Probability, 2008, 13 (25), pp.777-810. ⟨inria-00164758v2⟩



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